The spectra of matching polynomials which are useful in the computations of resonance energy and grand canonical partition functions of molecular's. It also present other properties for certain classes of graphs a...The spectra of matching polynomials which are useful in the computations of resonance energy and grand canonical partition functions of molecular's. It also present other properties for certain classes of graphs and lattices. In [1] Balasubramanian calculates several matching polynomials and matching roots of several molecular graphs. He found that the matching polynomial of C_6, C_(10), C_(14), C_(18) and C_(22) are divided by x^2-2. In this note,we prove that x^2-2 divides MC_(4k+2)(x), k = 1, 2,..., n and obtain some other properties of matching polynomials of paths and cycles.展开更多
基金Supported by the Natural Science Foundation of the People’s Republic of China under Grant（11571252）
文摘The spectra of matching polynomials which are useful in the computations of resonance energy and grand canonical partition functions of molecular's. It also present other properties for certain classes of graphs and lattices. In [1] Balasubramanian calculates several matching polynomials and matching roots of several molecular graphs. He found that the matching polynomial of C_6, C_(10), C_(14), C_(18) and C_(22) are divided by x^2-2. In this note,we prove that x^2-2 divides MC_(4k+2)(x), k = 1, 2,..., n and obtain some other properties of matching polynomials of paths and cycles.
基金Supported by the National Natural Science Foundation of China(11071151)the Natural Science Foundation of Qinghai Province(2011-Z-911)the Natural Science Foundation of Shaanxi Province(2010JM1005)
